Path classification and estimation method and system for prognosticating asset life

ABSTRACT

Path classification and estimation method and system used in combination with a computer and memory for prognosticating the remaining useful life of an asset by classifying a current degradation path of a current asset as belonging to one or more of previously collected degradation paths of exemplary assets and using the resulting classifications to estimate the remaining useful life of the current asset.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of (and claims the benefitof priority under 35 U.S.C. §§120 and 121 to) U.S. application Ser. No.12/315,117, filed Nov. 28, 2008, currently pending and which is herebyincorporated by reference herein in its entirety and which claimspriority under 35 USC Section 119(e) to U.S. Provisional PatentApplication No. 61/005,057, filed Nov. 30, 2007, the entire disclosureof which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

This invention relates generally to prognostic methods and systems, andin particular, to a path classification and estimation (PACE) method andsystem for prognosticating the remaining useful life (RUL) of an asset.

BACKGROUND OF THE INVENTION

In recent years, the field of prognostics has reached buzzword status.The result of which has been an avalanche of literature describing manydifferent prognostic algorithms that are supposedly capable ofestimating the remaining useful life (RUL) of an individual asset.However, upon closer examination, it is evident that the current stateof the art is cluttered with methods that either do not produceestimates of the RUL or do not provide a realistic method for relatingdegradation to the RUL.

For example, a general path model (GPM) (Lu, C. Joseph and William Q.Meeker, “Using Degradation Measures to Estimate a Time-to-FailureDistribution”, Technometrics, Vol. 35, No. 2, pp. 161-174: May 1993.) isfounded on the concept that a degradation signal collected from anindividual asset will follow a general path until it reaches anassociated failure threshold. Since its introduction, the thought modelproposed in the GPM has been prolifically adopted by modern researchersand has resulted in a plethora of techniques that can be related to theGPM in one way or another. Examples of these techniques can be found inthe following publications: Upadhyaya, Belle R., Masoud Naghedolfeizi,and B. Raychaudhuri, “Residual Life Estimation of Plant Components”,Periodic and Predictive Maintenance Technology, pages 22-29: June 1994;Mishra, S. and M. Pecht, “In-situ Sensors for Product ReliabilityMonitoring”, Proceedings of the SPIE, Vol. 4755, pages 10-19: 2002;Loecher, M. and C. Darken, “Concurrent Estimation of Time-to-Failure andEffective Wear”, Proceedings of the Maintenance and ReliabilityConference (MARCON), Knoxville, Tenn.: May 4-7, 2003; Mishra, S., S.Ganesan, M. Pecht and J. Xie, “Life Consumption Monitoring forElectronic Prognostics”, Proceedings of the IEEE Aerospace Conference,Vol. 5, pages 3455-3467: Mar. 6-13, 2004; Yan, Jihong, Muammer Koc, andJay Lee, “A Prognostic Algorithm for Machine Performance Assessment andIts Applications”, Production Planning & Control, Vol. 15, No. 8, pages796-801: December 2004; Xu, Di and Wenbiao Zhao, “Reliability Predictionusing Multivariate Degradation Data”, Proceedings of the AnnualReliability and Maintainability Symposium, pages 337-341, Alexandria,Va.: Jan. 24-27, 2005; Liao, Haitao, Wenbiao Zhao, and Huairui Guo,“Predicting Remaining Useful Life of an Individual Unit UsingProportional Hazards Model and Logistic Regression Model”, Proceedingsof the Reliability and Maintainability Symposium (RAMS), pages 127-132:Jan. 23-26, 2006; and Vichare, Nikhil M., and Michael G. Pecht,“Prognostic and Health Management of Electronics”, IEEE Transactions onComponents and Packaging Technologies, Vol. 29, No. 1, pages 222-229:March 2006.

Now, from the cursory description of the general path model (GPM)hereinabove, it can be seen that there are two fundamental assumptionsof the GPM and its modern counterparts: First, there exists a path forthe degradation signal that can be parameterized via regression, machinelearning, et cetera and secondly, there exists a failure threshold forthe degradation signal that accurately predicts when a asset will fail.For modern computational capacity, the first assumption is minor, inthat many methods exist for parameterizing simple (polynomialregression, power regression, et cetera) and complex (fuzzy inferencesystems, neural networks, et cetera) relationships from data. Theassumption of the existence of a threshold that accurately predictsasset failure is not so easily reconciled. While the existence of afailure threshold has been shown to be valid for well understooddegradation processes (for example, seeded crack growth) and controlledtesting environments (for example, constant load or uniform cycling),the above referenced publication to Liao, et al., titled “PredictingRemaining Useful Life of an Individual Unit Using Proportional HazardsModel and Logistic Regression Model” observes that for real worldapplications, where the failure modes are not always well understood orcan be too complex to be quantified by a single threshold, the failureboundary is vague at best. Wang, et al. attempt to address this problemby integrating uncertainty into the estimate of the threshold (Wang,Peng and David W. Coit, “Reliability and Degradation Modeling withRandom or Uncertain Failure Threshold”, Proceedings of the AnnualReliability and Maintainability Symposium, Las Vegas, Nev.: Jan. 28-31,2007), but in the end the authors replace an estimate of the thresholdwith another, more conservative estimate.

For the most part modern prognostic methods have failed to actuallyproduce estimates of the RUL; however, it is important to note thatthere are methods available that actually estimate the RUL of anindividual asset. For example, most notably Bonissone, et al.(Bonissone, P. and K. Goebel (2002), “When Will It Break? A Hybrid SoftComputing Model to Predict Time-to-Break Margins in Paper Machines”,Proceedings of SPIE 47th Annual Meeting, International Symposium onOptical Science and Technology, Vol. 4785, pages 53-64: 2002) use acomplex system involving many statistical and artificial intelligencebased methods to infer the RUL of a paper machine. However, the sheercomplexity and poor estimate accuracy limited the applicability of thiswork to an academic forum.

Hence, there is a need for a method and system for prognosticating theremaining useful life (RUL) of an asset that ameliorates or overcomesone or more of the shortcomings of the known prior art.

BRIEF SUMMARY OF THE INVENTION

Accordingly, and in one aspect, an embodiment of the inventionameliorates or overcomes one or more of the significant shortcomings ofthe known prior art by performing two main operations to estimate aremaining useful life (RUL) of an asset, namely classification andestimation. First, degradation of an asset is classified according toexpected/example asset degradations. Second, the remaining useful life(RUL) of the asset is estimated by combining class memberships withexpected/example remaining lifetimes.

More particularly, and in one aspect, an embodiment of the inventionprovides a path classification and estimation (PACE) method and systemfor prognosticating a remaining useful life (RUL) of an individual assetwherein observations of the individual asset's degradation areclassified according to previously acquired examples of assetdegradations and the result of the classification is used to estimatethe RUL of the individual asset. Hence, an embodiment of the inventionprovides a prognostic method and system that provides accurate estimatesof the RUL of an individual asset in many different contexts.

Additionally, and in another aspect, an embodiment of the inventionprovides a path classification and estimation (PACE) method and systemthat has extreme flexibility to incorporate multiple degradationsignals, degradation signals with and without failure thresholds, expertopinion, any degradation signal provided it can be represented as afunction that maps asset life to expected degradation signal values, andany inference procedure for classifying the degradation and/orestimating the RUL.

Furthermore, and in another aspect, an embodiment of the inventionprovides a prognostic method and system comprising path classificationand estimation (PACE) for prognosticating the remaining useful life(RUL) of an asset wherein a degradation signal of an individual asset isallowed to indicate life uniquely in stark contrast to the prior artmethod of concluding that the individual asset has failed if itsdegradation signal exceeds a chosen threshold.

In a further aspect, an embodiment of the invention provides acomputer-implemented method for estimating a remaining useful life of acurrent asset, comprising the steps of: obtaining exemplar degradationdata from at least two example assets; acquiring current assetdegradation data from a current asset; classifying the current assetdegradation data as a function of similarity between the current assetdegradation data and the exemplar degradation data; and estimating aremaining useful life of the current asset using results of theclassification step. Additionally, an embodiment of the inventionprovides a computer-readable medium having computer executableinstructions recorded thereon which causes, in use, a computer runningthe instructions to execute a procedure according to the abovecomputer-implemented method.

In another further aspect, an embodiment of the invention provides acomputer-implemented method for estimating a remaining useful life of acurrent asset, comprising the steps of: obtaining exemplar degradationdata from at least two example assets; transforming the exemplardegradation data into functional approximations defining exemplardegradation paths; acquiring current asset degradation data from acurrent asset; transforming the current asset degradation data into acurrent functional approximation defining a current asset degradationpath; classifying the current asset degradation data by determining aplurality of similarities each quantifying a degree of similarity of thecurrent asset degradation path to at least one of the exemplardegradation paths; and estimating a remaining useful life of the currentasset using the determined plurality of similarities. Additionally, anembodiment of the invention provides a computer-readable medium havingcomputer executable instructions recorded thereon which causes, in use,a computer running the instructions to execute a procedure according tothe above computer-implemented method.

In another further aspect, an embodiment of the invention provides acomputer-implemented method for estimating a remaining useful life of acurrent asset, comprising the steps of: obtaining exemplar degradationdata from at least two exemplar assets; constructing a vector ofexemplar failure times and a vector of functional approximations fromthe exemplar degradation data; acquiring observed degradation data froma current asset over a period of time that includes a defined time t;subtracting the defined time t from each of the exemplar failure timesfor obtaining a vector of expected remaining useful lives; evaluatingthe vector of functional approximations at the defined time t forobtaining a vector of expected degradation data values; evaluating theobserved degradation data at the defined time t for obtaining anobserved degradation data value; classifying the observed degradationdata value as a function of the expected degradation data values byassigning a membership value to each of the expected degradation datavalues as a function of similarity to the observed degradation datavalue for obtaining a vector of memberships; and combining the vector ofmemberships with the vector of expected remaining useful lives forestimating a remaining useful life value for the current asset.Additionally, an embodiment of the invention provides acomputer-readable medium having computer executable instructionsrecorded thereon which causes, in use, a computer running theinstructions to execute a procedure according to the abovecomputer-implemented method.

In another further aspect, an embodiment of the invention provides anasset surveillance system for estimating a remaining useful life of acurrent asset, said system comprising: means for obtaining exemplardegradation data from at least two example assets; a data acquisitiondevice for acquiring current asset degradation data from a currentasset; classification means for classifying said current assetdegradation data as a function of similarity between said current assetdegradation data and said exemplar degradation data; and means forestimating a remaining useful life of the current asset using results ofthe classification.

In another further aspect, an embodiment of the invention provides asystem for estimating a remaining useful life of a current asset, saidsystem comprising: means for obtaining exemplar degradation data from atleast two example assets; means for transforming the exemplardegradation data into functional approximations defining exemplardegradation paths; a data acquisition device for acquiring current assetdegradation data from a current asset; means for transforming thecurrent asset degradation data into a current functional approximationdefining a current asset degradation path; means for classifying thecurrent asset degradation data by determining a plurality ofsimilarities each quantifying a degree of similarity of the currentasset degradation path to at least one of the exemplar degradationpaths; and means for estimating a remaining useful life of the currentasset using the determined plurality of similarities.

In yet another further aspect, an embodiment of the invention provides asystem for estimating a remaining useful life of a current asset, saidsystem comprising: means for obtaining degradation data from at leasttwo exemplar assets; means for constructing a vector of exemplar failuretimes and a vector of functional approximations from the obtaineddegradation data; a data acquisition device for acquiring observeddegradation data from a current asset over a period of time thatincludes a defined time t; means for subtracting the defined time t fromeach of the exemplar failure times for obtaining a vector of expectedremaining useful lives; means for evaluating the vector of functionalapproximations at the defined time t for obtaining a vector of expecteddegradation data values; means for evaluating the observed degradationdata at the defined time t for obtaining an observed degradation datavalue; means for classifying the observed degradation data value as afunction of the expected degradation data values by assigning amembership value to each of the expected degradation data values as afunction of similarity to the observed degradation data value forobtaining a vector of memberships; and means for combining the vector ofmemberships with the vector of expected remaining useful lives forestimating a remaining useful life value for the current asset.

Accordingly, it should be apparent that numerous modifications andadaptations may be resorted to without departing from the scope and fairmeaning of the claims as set forth herein below following the detaileddescription of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of an embodiment of a pathclassification and estimation method and system for prognosticating theremaining useful life of an asset.

FIG. 2 is a functional flow diagram detailing an embodiment of atraining procedure of the path classification and estimation method andsystem for prognosticating the remaining useful life of an asset.

FIG. 3 is a functional flow diagram detailing an embodiment of anexecution procedure of the path classification and estimation method andsystem for prognosticating the remaining useful life of an asset.

FIG. 4 is a general flowchart view of an embodiment of acomputer-implemented method for estimating a remaining useful life of acurrent asset.

FIG. 5 is a flowchart view further detailing an embodiment of acomputer-implemented method for estimating a remaining useful life of acurrent asset.

FIG. 6 illustrates a plot of example degradation signals of exemplarassets.

FIG. 7 illustrates a plot of the example degradation signals of exemplarassets illustrated in FIG. 6 and their associated functionalapproximations shown by dashed lines.

FIG. 8 illustrates a plot of an observation of a degradation signal ofan asset at time t* relative to the functional approximations of theexemplar assets shown by dashed lines.

FIG. 9 is a general functional flow diagram detailing an embodiment of avector analysis procedure of the path classification and estimationmethod and system for estimating the remaining useful life of an asset.

FIG. 10 illustrates a top plot of the functional approximations of theexemplar assets shown by dashed lines and a complete query path of thedegradation signal shown in FIG. 8 and a bottom plot illustrating aprogression of the remaining useful life for the approximated exemplarpaths shown in dashed lines with the remaining useful life for the querypath of the degradation signal of the asset shown in solid.

FIG. 11 illustrates a plot of exemplar degradation signals of exampleassets having failure thresholds.

FIG. 12 illustrates a plot illustrating a process by which the exemplardegradation signals having failure thresholds can be modified for usewith the path classification and estimation method and system.

FIG. 13 is a general functional flow diagram detailing an embodiment ofa vector analysis procedure of the path classification and estimationmethod and system generalized for a number of degradation signals andexemplar degradation paths for estimating the remaining useful life ofan asset.

FIG. 14 is a flowchart view further detailing an embodiment of acomputer-implemented method for estimating a remaining useful life of acurrent asset.

FIG. 15 illustrates a summary table of prognoser accuracies for mudinvasion (MI) and pressure transducer offset (PTO) failures.

FIG. 16 illustrates a summary table of training and validationdegradation data for power supply assets which include a training powersupply (PS) number one, a training power supply (PS) number two, and avalidation power supply (PS).

FIG. 17 illustrates a plot of observed and regressed progression valuesfor training power supply number one.

FIG. 18 illustrates a plot of remaining useful life estimates and targetvalues for the validation power supply.

FIG. 19 illustrates a summary table of statistics for residual values(target values minus estimate values) of the remaining useful life ofthe validation power supply.

DETAILED DESCRIPTION OF THE INVENTION

Considering the drawings, wherein like reference numerals denote likeparts throughout the various drawing figures, reference numeral 10 isdirected to a path classification and estimation (PACE) method andsystem for prognosticating the remaining useful life (RUL) of an asset.

Referring to FIG. 1, and in one embodiment, the path classification andestimation (PACE) method and system 10 is comprised of an example assetdegradations procedure or training procedure 20 and an executionprocedure 40 which are, in one embodiment, implemented with softwarerunning on a computer 12 having an associated memory means 14 forprognosticating the remaining useful life (RUL) of at least one asset18.

More specifically, and referring to FIGS. 1 through 3, the method andsystem 10 includes the example asset degradations procedure or trainingprocedure 20 which initially performs an acquisition procedure 22 foracquiring example asset degradation signals or data 24 of at least twoexample assets (e.g., Example Asset Number 1 and Example Asset Number 2)and for storing the example asset degradation signals or data 24 inmemory means 14. The acquisition of the asset degradation signals ordata 24 from at least the two example assets can be provided by a dataacquisition, signal processing, and digitization means 16 electricallycoupled between the computer 12 and at least the two example assets. Theasset degradation signals or data 24 can also be acquired by memorymeans 14 of the computer 12 via, for example, user input means 26,memory input means 27, and/or remote computer means 28. Once acquired,the asset degradations procedure or training procedure 20 determinesshapes of asset degradations and times at which the example assets failfrom the example asset degradation signals or data 24.

In particular, and referring to FIGS. 1 and 2, the example assetdegradations procedure or training procedure 20 performs anapproximation procedure 30 for approximating the example assetdegradation signals or data 24 with functions (polynomial, neuralnetwork, et cetera) for defining example asset degradation paths 32 andstoring the example asset degradation paths 32 in memory means 14.Additionally, the example asset degradations procedure or trainingprocedure 20 performs an extraction procedure 34 for extracting failuretimes from the example asset degradation signals or data 24 for definingexample asset failure times 36 and for storing the example asset failuretimes 36 in memory means 14.

Referring now to FIGS. 1 and 3, the method and system 10 furtherincludes the execution procedure 40 which employs the stored functionsthat represent the example asset degradation paths 32 and the associatedexample asset failure times 36 for prognosticating the remaining usefullife (RUL) of another asset such as at least the one asset 18. In oneembodiment, the execution procedure 40 starts with an extractionprocedure 42 for extracting a current use time 44 from at least the oneasset 18 and an extraction procedure 46 for extracting current assetdegradation signals or data 48 from at least the one asset 18. Thecurrent use time 44 and the current asset degradation signals/data 48can be acquired by the computer 12 and thus, by memory means 14 via, forexample, the data acquisition, signal processing, and digitization means16 electrically coupled between the computer 12 and at least the oneasset 18, user input means 26 electrically coupled to the computer 12,memory input means 27 electrically coupled to the computer 12, and/orremote computer means 28 electrically coupled to the computer 12.

Next, the execution procedure 40 performs an evaluation procedure 50comprised of evaluating functional approximations of the example assetdegradation paths 32 at the current use time 44 to obtain expected assetdegradations 52. The execution procedure 40 also performs a subtractionprocedure 54 comprised of subtracting the current use time 44 from theexample asset failure times 36 to obtain expected asset remaining usefullives 56. At this point, the execution procedure 40 performs aclassification procedure 58 comprised of classifying the current assetdegradation 48 according to the expected asset degradations 52. Inparticular, and in one embodiment, the execution process 40 performs theclassification procedure 58 comprised of classifying the current assetdegradation 48 of at least the one asset 18 by determining a pluralityof similarities that each quantify how similar the current assetdegradation 48 is to each of the previously collected examples orfunctions that represent the example asset degradation paths 32 forobtaining similarities of current to expected asset degradations 60.Finally, the execution procedure 40 performs a estimate remaining usefullife procedure or estimation procedure 62 comprised of combining theplurality of similarities of current to expected asset degradations 60with the expected asset remaining useful lives 56 for obtaining anestimation or prognostication of the remaining useful life 64 of atleast the one asset 18.

Accordingly, and in one aspect, FIG. 4 illustrates a general flowchartview of an embodiment of a computer-implemented method for estimating aremaining useful life of the current asset 18. Additionally, anembodiment of the invention provides a computer-readable medium 68having computer executable instructions recorded thereon which causes,in use, the computer 12 running the instructions to generally execute aprocedure according to the computer-implemented method illustrated inFIG. 4.

In another aspect, FIG. 5 illustrates a flowchart view further detailingan embodiment of a computer-implemented method for estimating aremaining useful life of the current asset 18. Additionally, anembodiment of the invention provides the computer-readable medium 68having computer executable instructions recorded thereon which causes,in use, the computer 12 running the instructions to generally execute aprocedure according to the computer-implemented method illustrated inFIG. 5.

Generally, any type of computer readable medium 68 may be employed andexamples include floppy disks, hard disks, CD-ROMS, Flash ROMS,nonvolatile ROM, and RAM. Additionally, the memory means 14 may beemployed for the computer readable medium 68.

Furthermore, and in an embodiment of the invention, acomputer-implemented method for estimating the remaining useful life ofthe current asset 18 can further include one or more of the followingsteps: communicating the estimated remaining useful life of the currentasset to a remote computer 28, sounding an alarm 29 when an alarm actionis determined to be necessitated as a function of the remaining usefullife of the current asset 18; performing a control action, via assetcontrol means 31, on the current asset 18 when determined to benecessitated as a function of the remaining useful life of the currentasset 18; and/or displaying the estimated remaining useful life of thecurrent asset on a display 66.

Moreover, examples of degradation signals include but are not limited tothe cumulative absorbed vibration energy, number of thermal cycles,number of uses, number of alarms, magnitude of difference between apredicted parameter and a corresponding observed parameter, cumulativedifference between a predicted parameter and a corresponding observedparameter, frequency of fault or anomaly events, cumulative number offault or anomaly events, measured or computed efficiency (for examplepumping efficiency), rate of change of efficiency, output voltage duringdischarge for a battery, amplitude of Lamb waves measured bypiezoelectric transducers in a structure, switching transient gatevoltage in a gate controlled transistor, tumor mass, cumulativecigarette consumption, et cetera. Thus, the degradation signal orsignals are a type which will now be evident to those having ordinaryskill in the art, informed by the present disclosure.

Now that a high level description of the path classification andestimation (PACE) method and system 10 has been presented hereinabove, afurther detailed delineation of the path classification and estimation(PACE) method and system 10 will be presented hereinbelow which willthen be followed by a description of exemplary applications.

As its name suggests, the path classification and estimation (PACE)method and system 10 is fundamentally comprised of two operations: 1)classifying a current degradation path as belonging to one or more ofpreviously collected exemplar degradation paths and 2) using theresulting classifications to estimate the RUL. Hence, the name pathclassification (classify path according to exemplar paths) andestimation (estimate the RUL from the results of the classification). Atthis point, the PACE is described in more detail by considering ahypothetical example.

Illustrative Example

To begin, consider the example degradation signals presented in FIGS. 6and 7. The degradation signals U₁(t), U₂(t), U₃(t), and U₄(t) and theirassociated failure times T₁, T₂, T₃, and T₄ are presented in the FIG. 6.Here, the failure times are set to be either the time that the assetfails or the time at which someone determines that the asset performancehas sufficiently degraded such that it has effectively failed. For thisexample, it can be seen that there is not a clear failure threshold forthe degradation signal. In the FIG. 7, the paths are generalized byfitting an arbitrary function to the data via regression, machinelearning, et cetera, for obtaining functional approximations ƒ₁(t,θ₁),ƒ₂(t,θ₂), ƒ₃(t,θ₃), and ƒ₄(t,θ₄). There are two items of informationthat are extracted or derived from the degradation paths, specificallythe failure times and the shape of the degradation that is described bythe functional approximations. These items of information are used toconstruct a vector of exemplar failure times 36 and functionalapproximations providing example asset degradation paths 32, as follows:

$\begin{matrix}{T = {{\begin{bmatrix}T_{1} \\T_{2} \\T_{3} \\T_{4}\end{bmatrix}\mspace{14mu}{f\left( {t,\Theta} \right)}} = \begin{bmatrix}{f_{1}\left( {t,\theta_{1}} \right)} \\{f_{2}\left( {t,\theta_{2}} \right)} \\{f_{3}\left( {t,\theta_{3}} \right)} \\{f_{4}\left( {t,\theta_{4}} \right)}\end{bmatrix}}} & ({E1})\end{matrix}$

Here, T_(i) and fƒ_(i)(t,θ_(i)) are the failure times and functionalapproximation of the i^(th) exemplar degradation signal pathrespectively, θ_(i) are the parameters of the functional approximationof the i^(th) exemplar degradation signal path, and Θ are all of theparameters of each functional approximation.

To employ the method and system 10, the degradation signal of another,similar asset (e.g., at least the one asset 18) is monitored and anestimate of the remaining useful life 64 of the similar asset isdetermined at an arbitrary time t*. Such a case is presented in FIG. 8,where the degradation signal is plotted as a solid path 72. Theobservation of the degradation signal at time t* is written as u(t*). Toestimate the remaining useful life 64 of the similar asset via the pathclassification and estimation (PACE) method and system 10, the processpresented in FIG. 9 is used.

In general, and referring to FIG. 9, the process for estimating theremaining useful life 64 can be seen to be comprised of three steps.First, the expected degradation signal values according to the exemplardegradation paths are estimated by evaluating the functionalapproximations functions at t*. At the same time, the expected remaininguseful lives are calculated by subtracting the current time t* from theobserved failure times of the exemplar paths. Second, the observeddegradation signal u(t*) is then classified according to the vector ofexpected degradation signal values U(t*). The new degradation path isassigned a membership value for each of the historical paths thatcharacterizes it's similarity to that exemplar. Third, the vector ofmemberships of the observed degradation value to the exemplardegradation paths is combined with the vector of expected remaininguseful lives to estimate the remaining useful life of the similar assetspace l(t*).

Further details of the path classification and estimation (PACE) methodand system 10 will now be described hereinbelow in the context of thepresent example.

First, the current time t* is used to estimate the expected values ofthe degradation signal and remaining useful lives according to theexemplar paths. In equation form, the expected values of the degradationsignal according to the exemplar paths are the approximating functionsevaluated at the current time t*.

$\begin{matrix}{{f\left( {t^{*},\Theta} \right)} = \begin{bmatrix}{f_{1}\left( {t^{*},\theta_{1}} \right)} \\{f_{2}\left( {t^{*},\theta_{2}} \right)} \\{f_{3}\left( {t^{*},\theta_{3}} \right)} \\{f_{4}\left( {t^{*},\theta_{4}} \right)}\end{bmatrix}} & ({E2})\end{matrix}$

The function evaluations can be interpreted as exemplars of thedegradation signal values at time t*. In this context, the above vectorcan be rewritten as a follows:

$\begin{matrix}{{U\left( t^{*} \right)} = {\begin{bmatrix}{f_{1}\left( {t^{*},\theta_{1}} \right)} \\{f_{2}\left( {t^{*},\theta_{2}} \right)} \\{f_{3}\left( {t^{*},\theta_{3}} \right)} \\{f_{4}\left( {t^{*},\theta_{4}} \right)}\end{bmatrix} = \begin{bmatrix}{U_{1}\left( t^{*} \right)} \\{U_{2}\left( t^{*} \right)} \\{U_{3}\left( t^{*} \right)} \\{U_{4}\left( t^{*} \right)}\end{bmatrix}}} & ({E3})\end{matrix}$

The current time t* is used with the vector of failure times tocalculate the expected remaining useful lives according to the exemplardegradation paths.

$\begin{matrix}{{{L\left( t^{*} \right)} = {{T - t^{*}} = \begin{bmatrix}{T_{1} - t^{*}} \\{T_{2} - t^{*}} \\{T_{3} - t^{*}} \\{T_{4} - t^{*}}\end{bmatrix}}}\mspace{11mu}} & ({E4})\end{matrix}$

Now the currently observed degradation signal value u(t*) can becompared to the expected degradation signal values U(t*) by any one of anumber of known classification methods (e.g., clustering, nearestneighbor, k-nearest neighbor, non-parametric regression, fuzzy logic,neural networks, et cetera) to obtain a vector of membershipsμ_(U)[u(t*)]. Here, μ_(U) _(i) [u(t*)] denotes the membership of u(t*)to the i^(th) exemplar path.

$\begin{matrix}{{\mu_{U}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} = \begin{bmatrix}{\mu_{U_{1}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} \\{\mu_{U_{2}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} \\{\mu_{U_{3}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} \\{\mu_{U_{4}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack}\end{bmatrix}} & ({E5})\end{matrix}$

Finally, the above memberships and the expected remaining useful livesare combined to estimate the current remaining useful life l(t*) of theindividual asset. For example, a simple weighted average could be used.To construct the simple weighted average, the memberships could becalculated to have values on [0,1] or scalar values between 0 and 1 withthe sum of the memberships normalized to a value of 1. The weightedaverage remaining useful life is then given by the following:

${l\left( t^{*} \right)} = {\sum\limits_{i}^{n}\left( {{\mu_{U_{i}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} \cdot {L_{i}\left( t^{*} \right)}} \right)}$

Other combination methods include: selecting the example RUL that hasthe highest membership, setting the RUL to be an average of the klargest memberships, using statistical and/or machine learning (i.e.neural networks, fuzzy logic, et cetera) to infer the RUL from thememberships and other factors such as environmental signals, qualityfactors for each example path (better examples have larger qualityfactors), or combining a weighted average with an example selector thatis affected by the operating conditions. For example, it is possiblethat the method and system 10 would only use examples 1, 3, and 10 forone operating condition and examples 2, 4, and 12 for a differentoperating condition.

Now that the general process for estimating the remaining useful life atan arbitrary time t* via the path classification and estimation (PACE)method and system 10 has been discussed, the character of the estimateswill now be explored. To describe the character of the estimates of thepath classification and estimation (PACE) method and system 10estimates, consider the complete query path of the degradation signalthat is presented in the top plot of FIG. 10. The path classificationand estimation (PACE) method and system 10 estimates of the remaininguseful life are presented in the bottom plot, where the dashed linesdesignate the progression of the remaining useful life for theapproximated exemplar paths. As a starting point, consider the time from0 to t₁. Notice that during this time period, the observed degradationsignal values (solid line 74) are very near the functional approximationof the second exemplar path (dashed line 78). What this means is thatthe query path is very similar to the second exemplar path. It can beseen in the bottom plot that this affinity is reflected in the remaininguseful life estimates, which are very near the expected remaining usefullives for the second exemplar path. Next, consider the time between t₁and t₂. During this time period, the query path of the degradationsignal can be observed to move toward the third exemplar path (dashedline 80). The remaining useful life estimates can be seen to respond tothis change by trending away from the remaining useful lives of thesecond exemplar path (dashed line 78) and toward the third exemplar path(dashed line 80). Finally, consider the time between t₂ and t₃. Noticethat the failure time of the query asset is t₃. During this timeinterval, notice that the query path of the degradation signal can beobserved to move toward the fourth exemplar path (dashed line 82).Again, this shift is reflected in the remaining useful life estimates,which shifts toward the remaining useful lives of the fourth exemplarpath.

Modification for a Known Failure Threshold

Before the path classification and estimation (PACE) method and system10 is generalized, the case when a failure threshold for the degradationsignal is previously known will be considered. For the working example,suppose that the failure threshold is U_(f). Since the pathclassification and estimation (PACE) method and system 10 does notrequire a threshold, the original degradation signals and theirassociated failure times will be adjusted before they are used with thepath classification and estimation (PACE) method and system 10.

FIGS. 11 and 12 present a demonstration of this process. Specifically,the original signals are presented in the top plot and the adjustedsignals are presented in the bottom plot. It can be seen that theoriginal degradation signals U_(i)(t) are “clipped” at the failurethreshold resulting in the adjusted degradation signals U*_(i)(t) whosemaximum value is U_(f). Next, notice that the failure times are alsoadjusted to the times when the adjusted degradation signals reach thethreshold. More specifically, the adjusted failure times for the i^(th)exemplar degradation signal are set according to the following equation.U* _(i)(T* _(i))=U _(f)  (E6)

A description of the PACE as it applies to a simple example waspresented hereinabove.

Hereinbelow, the equations developed above are generalized for anarbitrary number of exemplar histories and degradation signals.Additionally, FIG. 13 illustrates a general functional flow diagramdetailing an embodiment of a vector analysis procedure of the pathclassification and estimation method and system generalized for a numberof degradation signals and exemplar degradation paths for estimating theremaining useful life of an asset.

Generalized PACE

More specifically, the previously developed equations are generalizedfor p degradation signals and for n exemplar degradation paths. For thiscase, the exemplar degradation paths can be characterized by thefollowing matrix of functional approximations:

$\begin{matrix}{{f\left( {t,\Theta} \right)} = \begin{bmatrix}{f_{1,1}\left( {t,\theta_{1,1}} \right)} & {f_{1,2}\left( {t,\theta_{1,2}} \right)} & \ldots & {f_{1,p}\left( {t,\theta_{1,p}} \right)} \\{f_{2,1}\left( {t,\theta_{2,1}} \right)} & {f_{2,2}\left( {t,\theta_{2,2}} \right)} & \ldots & {f_{2,p}\left( {t,\theta_{2,p}} \right)} \\\vdots & \vdots & \ddots & \vdots \\{f_{n,1}\left( {t,\theta_{n,1}} \right)} & {f_{n,2}\left( {t,\theta_{n,2}} \right)} & \ldots & {f_{n,p}\left( {t,\theta_{n,p}} \right)}\end{bmatrix}} & ({E7})\end{matrix}$

where:

ƒ_(i,j)(t,θ_(i,j)) is the functional approximation of the j^(th)degradation signal of the i^(th) exemplar history;

θ_(i,j) are the parameters of the functional approximation of the j^(th)degradation signal of the i^(th) exemplar history; and

Θ are all of the parameters of each functional approximation.

For each of the n exemplar paths, there is an associated failure time.If T_(i) denotes the failure time of the i^(th) exemplar path, then thevector of failure times can be written as:

$\begin{matrix}{T = {\begin{bmatrix}T_{1} \\T_{2} \\\vdots \\T_{n}\end{bmatrix}\;.}} & ({E8})\end{matrix}$

At this point, suppose that the p degradation signals of another similarasset are being monitored and an estimate of the remaining useful lifeof the similar asset is needed at an arbitrary time t*. First, thecurrent time t* is used to estimate the expected values of thedegradation signals and remaining useful lives according to the nexemplar paths. In equation form, the expected values of the pdegradation signals according to the n exemplar paths are simply theapproximating functions evaluated at the current time t*.

$\begin{matrix}{{f\left( {t^{*},\Theta} \right)} = \begin{bmatrix}{f_{1,1}\left( {t^{*},\theta_{1,1}} \right)} & {f_{1,2}\left( {t^{*},\theta_{1,2}} \right)} & \ldots & {f_{1,p}\left( {t^{*},\theta_{1,p}} \right)} \\{f_{2,1}\left( {t^{*},\theta_{2,1}} \right)} & {f_{2,2}\left( {t^{*},\theta_{2,2}} \right)} & \ldots & {f_{2,p}\left( {t^{*},\theta_{2,p}} \right)} \\\vdots & \vdots & \ddots & \vdots \\{f_{n,1}\left( {t^{*},\theta_{n,1}} \right)} & {f_{n,2}\left( {t^{*},\theta_{n,2}} \right)} & \ldots & {f_{n,p}\left( {t^{*},\theta_{n,p}} \right)}\end{bmatrix}} & ({E9})\end{matrix}$

The values of the above function evaluations can be interpreted asexemplars of the p degradation signals at time t*. In this context, theabove vector can be rewritten by the following equations, where U_(i,j)is the j^(th) degradation signal of the i^(th) exemplar path.

$\begin{matrix}{{{U\left( t^{*} \right)} = \begin{bmatrix}{f_{1,1}\left( {t^{*},\theta_{1,1}} \right)} & {f_{1,2}\left( {t^{*},\theta_{1,2}} \right)} & \ldots & {f_{1,p}\left( {t^{*},\theta_{1,p}} \right)} \\{f_{2,1}\left( {t^{*},\theta_{2,1}} \right)} & {f_{2,2}\left( {t^{*},\theta_{2,2}} \right)} & \ldots & {f_{2,p}\left( {t^{*},\theta_{2,p}} \right)} \\\vdots & \vdots & \ddots & \vdots \\{f_{n,1}\left( {t^{*},\theta_{n,1}} \right)} & {f_{n,2}\left( {t^{*},\theta_{n,2}} \right)} & \ldots & {f_{n,p}\left( {t^{*},\theta_{n,p}} \right)}\end{bmatrix}}{{U\left( t^{*} \right)} = \begin{bmatrix}{U_{1,1}\left( {t^{*},\theta_{1,1}} \right)} & {U_{1,2}\left( {t^{*},\theta_{1,2}} \right)} & \ldots & {U_{1,p}\left( {t^{*},\theta_{1,p}} \right)} \\{U_{2,1}\left( {t^{*},\theta_{2,1}} \right)} & {U_{2,2}\left( {t^{*},\theta_{2,2}} \right)} & \ldots & {U_{2,p}\left( {t^{*},\theta_{2,p}} \right)} \\\vdots & \vdots & \ddots & \vdots \\{U_{n,1}\left( {t^{*},\theta_{n,1}} \right)} & {U_{n,2}\left( {t^{*},\theta_{n,2}} \right)} & \ldots & {U_{n,p}\left( {t^{*},\theta_{n,p}} \right)}\end{bmatrix}}} & ({E10})\end{matrix}$

At the same time, the current time t* is used with the vector of failuretimes to calculate the expected remaining useful lives according to theexemplar degradation paths.

$\begin{matrix}{{L\left( t^{*} \right)} = {{T - t^{*}} = \begin{bmatrix}{T_{1} - t^{*}} \\{T_{2} - t^{*}} \\\vdots \\{T_{n} - t^{*}}\end{bmatrix}}} & ({E11})\end{matrix}$

The currently observed values for the p degradation signals can bewritten as a vector u(t*), where u_(j)(t*) is the currently observedvalue for the j^(th) degradation signal.u(t*)=[u ₁(t*)u ₂(t*) . . . u _(p)(t*)]  (E12)

The values contained in u(t*) can be compared to the expecteddegradation signal values U(t*) by any one of a number of classificationalgorithms to obtain a vector of memberships μ_(U)[u(t*)]. Here, μ_(U)_(i) [u(t*)] denotes the membership of u(t*) to the i^(th) exemplarpath. Notice that the memberships are a vector and not a matrix. Whatthis means is that the classification algorithm has aggregated thesimilarities contained in the p degradation signal observations todetermine the overall membership or similarity between the query andeach exemplar path. This feature is important when considering the wayin which different inference algorithms are integrated into the pathclassification and estimation (PACE) method and system 10.

$\begin{matrix}{{\mu_{U}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} = \begin{bmatrix}{\mu_{U_{1}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} \\{\mu_{U_{2}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} \\\vdots \\{\mu_{U_{4}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack}\end{bmatrix}} & ({E13})\end{matrix}$

Finally, the above memberships and the expected remaining useful livesare combined to estimate the current remaining useful life l(t*) of theindividual asset. For example, a simple weighted average could be used.To construct the simple weighted average, the memberships could becalculated to have values on [0,1] or scalar values between 0 and 1 withthe sum of the memberships normalized to a value of 1. The weightedaverage remaining useful life is then given by the following:

${l\left( t^{*} \right)} = {\sum\limits_{i}^{n}\left( {{\mu_{U_{i}}\left\lbrack {u\left( t^{*} \right)} \right\rbrack} \cdot {L_{i}\left( t^{*} \right)}} \right)}$

Combination methods include: simple weighted average, selecting theexample RUL that has the highest membership, setting the RUL to be anaverage of the k largest memberships, using statistical and/or machinelearning (i.e. neural networks, fuzzy logic, et cetera) to infer the RULfrom the memberships and other factors such as environmental signals,quality factors for each example path (better examples have largerquality factors), or combining a weighted average with an exampleselector that is affected by the operating conditions. For example, itis possible that the method and system 10 would only use examples 1, 3,and 10 for one operating condition and examples 2, 4, and 12 for adifferent operating condition.

Hereinabove, the path classification and estimation (PACE) method andsystem 10 was generalized to include an arbitrary number of degradationsignals and exemplar paths. Hereinbelow, some advantages of the pathclassification and estimation (PACE) method and system 10 will beenumerated.

Advantages of the PACE

In one aspect, an advantage of the path classification and estimation(PACE) method and system 10 as opposed to the other prognostic methodsis that a failure threshold is not required. This advantage is realizedfor applications where a failure threshold is not previously known orcannot be accurately estimated from collected data or engineeringjudgment.

In another aspect, an advantage of the path classification andestimation (PACE) method and system 10 is that if the failure thresholdis known ahead of time, the only modification that needs to be made isthat associated failure times need only be adjusted such thatdegradation signal values that exceed the threshold are interpreted ashaving failed.

In another aspect, an advantage of the path classification andestimation (PACE) method and system 10 is that it is flexible enough todynamically track changes in asset behavior that would result in amarked change in the remaining useful life estimates. To illustrate thisadvantage, in life consumption modeling (LCM) as a asset is used itsdegradation fraction monotonically increases thereby producingmonotonically decreasing remaining useful life estimates. What thismeans is that as an asset is used, its remaining useful life will alwaysdecrease. This assumption limits the LCM method in that no mechanism isprovided for allowing the remaining useful life estimates to correctthemselves. In other words, if the degradation is estimated to progressalong a fast failure mode, but then moves to a slower failure mode,there is no way to compensate for any errors in the remaining usefullife estimates that could have been incurred during the time required todetect the shift in degradation rate. In contrast to these shortcomings,the path classification and estimation (PACE) method and system 10 isable to reflect changes in degradation that lead to changes in theremaining useful life estimates.

In another aspect, an advantage of the path classification andestimation (PACE) method and system 10 is that since the individualanalysis procedures are founded on general concepts, such as functionapproximation, classification, and estimation, there is not a limitationon the algorithm types used for the individual analysis procedures.

In yet another aspect, an advantage of the path classification andestimation (PACE) method and system 10 is its flexibility to incorporatephysical simulations of degradation and expert opinion into its exampledata. Hence, the reliance on the existence of a sample of thedegradation paths is effectively transformed into an advantage in thesense that alternative individual based prognosis algorithms do notprovide a means for incorporating sparse information.

Accordingly, and in one aspect, FIG. 14 illustrates a detailed flowchartview of an embodiment of a computer-implemented method for estimating aremaining useful life of the current asset 18. Additionally, anembodiment of the invention provides a computer-readable medium 68having computer executable instructions recorded thereon which causes,in use, the computer 12 running the instructions to generally execute aprocedure according to the computer-implemented method illustrated inFIG. 14.

Exemplary Applications

In use and operation, and referring to FIGS. 1 through 19, the pathclassification and estimation (PACE) method and system 10 will befurther exemplified from the results of its use and operation inestimating the remaining useful life of individual steering systems ofdeep oil exploration drills and enterprise class server power supplies.The results of these applications are presented hereinbelow.

Steering System

For this work multiple prognosers were developed for two fault modes,namely mud invasion (MI) and pressure transducer offset (PTO). The firstprognoser is a population prognoser that estimates the remaining usefullife (RUL) via a conditional mean of the population's time-to-failuredistribution. The second prognoser is a path classification andestimation (PACE) prognoser trained to relate the cumulative vibrationstress to the RUL. Finally, the third prognoser is a PACE prognosertrained to relate the cumulative number of fault alarms to the RUL.

A summary of the accuracy of the population, causal, and effectprognosers is presented in FIG. 15. The mean absolute error (MAE) of theRUL estimates in hours is presented in the left column of the table. Thelife of the asset in hours is presented in the middle column. Next, theMAE as a percentage of the asset life is presented in the right columnof the table. Finally, MI and PTO designate two failure modes of thedrill's hydraulic units, namely mud invasion and pressure transduceroffset, respectively.

There are several features of the results that bear mentioning. Overall,notice that the individual based prognosers (causal and effect)significantly outperform the population based prognosers, in that theMAE as a percentage of the asset life ranges from 53-60% for thepopulation prognosers and ranges from 0.8-13% for the individual basedprognosers. What this means is that the individual based prognosers areable to predict the time of failure more accurately than the populationprognoser. Next, notice that there is a general trend in the MAE overall of the prognosers that begins with large errors for the populationbased prognoser, progresses toward intermediate errors for the causalprognoser, and then finally reaches a minimum error for the effectprognoser. This trend, however, is not complete, in that the smallesterror for the PTO is produced by the causal prognoser at 2.4% of theasset life, while the intermediate error is produced by the effectprognoser at 13.2%.

Server Power Supplies

Three power supplies (PS) were successfully cycled until failure. Foreach of these sets, a monitoring system was used to generate thedegradation signal (cumulative sum of the fault alarms). Next,onset-to-failure (OTF) is defined as being the instant in time when 500fault alarms have been registered. The degradation is parameterized bylinear regression of the degradation onto the time after OTF. Other,more complicated, regression functions were applied to the data, but itwas found that standard linear regression was sufficient to produceaccurate RUL estimates. Also, it is important to note that prior toperforming the regression, 500 was subtracted from each history to forcethe regressed line through the origin.

A summary of the two histories that were used to train the PACEprognoser and the validation history are presented in FIG. 16. Anexample degradation history and its associated regressed values are alsopresented in FIG. 17. The dashed plot 110 is the observed progressionand the solid plot 112 is the regressed progression.

Finally, the RUL was estimated by providing the trained PACE prognoserwith observations of the prognostic parameter for the validation PS. Theresulting RUL estimates (solid plot 114) and their target values (dashedplot 116) are presented in FIG. 18. The progression of the trainingpower supplies are also presented as dashed plots 118 and 120. Noticethat the RUL estimates begin by sharply oscillating between the firstand second training power supply. As the degradation continues, it canbe seen that the RUL estimates approach their target values beginningaround the 5^(th) hour after OTF. Since these estimates are made byconsidering only two degradation histories, as more data is madeavailable the performance should improve significantly.

Finally, to assess the uncertainties of the estimates, the statistics ofthe residuals (target−estimates) were calculated and are listed below inFIG. 19. As expected, the distribution of the errors is very large,mainly 95% of the error is contained on negative 2.47 days to positive3.34 days. This indicates that 95% of the time, the RUL estimate will beeither overestimated by approximately 2.5 days or underestimated byapproximately 3.3 days. However, a beneficial feature of this result isthat the RUL estimate improves over time. To illustrate this feature,consider the summary statistics for the first and second half of thedata as presented in the bottom two rows of FIG. 19. Because theestimates on the first half of the data swing sharply from overestimating to under estimating the RUL, the associated uncertaintybounds cover a range of approximately 7.53 days. Conversely, the summarystatistics for the second half of the data show that the range hasdecreased by approximately 47% to 3.96 days.

To conclude this discussion, the mean absolute error (MAE) of the RULestimates is evaluated. Overall, the MAE was calculated to be 1.35 days.In terms of the lifetime after OTF (10.71 days), the MAE was calculatedto be 12.6%. The accuracies for the first and second half of thedegradation history give MAEs of 2.03 days (19.0% of the lifetime afterOTF) and 0.66 days (6.2% of the lifetime after OTF), respectively.

These exemplary applications have demonstrated that the pathclassification and estimation (PACE) method and system 10 can be used toproduce accurate estimates of the RUL of an individual asset.

Accordingly, it should be apparent that further numerous structuralmodifications and adaptations may be resorted to without departing fromthe scope and fair meaning of the present invention as set forthhereinabove and as described herein below by the claims.

I claim:
 1. A computer-implemented method for estimating a remaining useful life of a current asset, comprising the steps of: obtaining exemplar degradation data from at least two example assets; transforming the exemplar degradation data into functional approximations defining exemplar degradation paths; acquiring current degradation data from a current asset; evaluating the functional approximations defining the exemplar degradation paths utilizing the current degradation data for obtaining expected degradation data; classifying the current degradation data as a function of similarity between the current degradation data and the expected degradation data; and estimating, with a computer, a remaining useful life of the current asset using results of the classification step.
 2. The computer-implemented method of claim 1 wherein the obtaining step includes obtaining the exemplar degradation data from at least one degradation signal from each of the at least two example assets.
 3. The computer-implemented method of claim 1 wherein the acquiring step includes acquiring the current degradation data from at least one degradation signal from the current asset.
 4. The computer-implemented method of claim 1 wherein the classifying step includes classifying the current degradation data as a function of similarity between the current degradation data and a functional approximation of the expected degradation data.
 5. The computer-implemented method of claim 1 wherein the estimating step includes using at least one asset failure time extracted from the exemplar degradation data along with the results of the classification step for estimating the remaining useful life of the current asset.
 6. The computer-implemented method of claim 1 further comprising a step of modifying the exemplar degradation data to accommodate a failure threshold.
 7. The computer-implemented method of claim 1 further comprising a step of communicating the estimated remaining useful life of the current asset to a remote computer.
 8. The computer-implemented method of claim 1 further comprising a step of displaying the estimated remaining useful life of the current asset on a display.
 9. The computer-implemented method of claim 1 further comprising a step of effecting a control action as a function of the estimated remaining useful life of the current asset.
 10. The computer-implemented method of claim 1 further comprising a step effecting an alarm action as a function of the estimated remaining useful life of the current asset.
 11. A non-transitory computer-readable medium having computer executable instructions for performing a method for estimating a remaining useful life of a current asset, the method comprising the steps of: obtaining exemplar degradation data from at least two example assets; transforming the exemplar degradation data into functional approximations defining exemplar degradation paths; acquiring current degradation data from a current asset; evaluating the functional approximations defining the exemplar degradation paths utilizing the current degradation data for obtaining expected degradation data; classifying the current degradation data as a function of similarity between the current degradation data and the expected degradation data; and estimating a remaining useful life of the current asset using results of the classification step.
 12. The non-transitory computer-readable medium of claim 11 wherein the obtaining step includes obtaining exemplar degradation data from at least one degradation signal from each of the at least two example assets.
 13. The non-transitory computer-readable medium of claim 11 wherein the acquiring step includes acquiring current degradation data from at least one degradation signal from the current asset.
 14. The non-transitory computer-readable medium of claim 11 wherein the classifying step includes classifying the current degradation data as a function of similarity between the current degradation data and a functional approximation of the expected degradation data.
 15. The non-transitory computer-readable medium of claim 11 wherein the estimating step includes using at least one asset failure time extracted from the exemplar degradation data along with using the results of the classification step for estimating the remaining useful life of the current asset.
 16. The non-transitory computer-readable medium of claim 11 wherein the method further comprises a step of modifying the exemplar degradation data to accommodate a failure threshold.
 17. The non-transitory computer-readable medium of claim 11 wherein the method further comprises a step of communicating the estimated remaining useful life of the current asset to a remote computer.
 18. The non-transitory computer-readable medium of claim 11 wherein the method further comprises a step of displaying the estimated remaining useful life of the current asset on a display.
 19. The non-transitory computer-readable medium of claim 11 wherein the method further comprises a step of effecting a control action as a function of the estimated remaining useful life of the current asset.
 20. The non-transitory computer-readable medium of claim 11 wherein the method further comprises a step effecting an alarm action as a function of the estimated remaining useful life of the current asset.
 21. A computer-implemented method for estimating a remaining useful life of a current asset, comprising the steps of: obtaining exemplar degradation data from at least two example assets; transforming the exemplar degradation data into functional approximations defining exemplar degradation paths; acquiring current degradation data from a current asset; evaluating the functional approximations defining the exemplar degradation paths utilizing the current degradation data for obtaining expected degradation data; determining the similarities between the current degradation data and the expected degradation data; and estimating, with a computer, a remaining useful life of the current asset using results of the determining step.
 22. A computer-implemented method for estimating a remaining useful life of a current asset, comprising the steps of: obtaining exemplar degradation data from at least two example assets; transforming the exemplar degradation data into functional approximations defining exemplar degradation paths; acquiring current degradation data from a current asset; evaluating the functional approximations defining the exemplar degradation paths at a current usage value to obtain expected degradation data; classifying the current degradation data as a function of similarity between the current degradation data and the expected degradation data; and estimating, with a computer, a remaining useful life of the current asset using results of the classifying step.
 23. A computer-implemented method for estimating a remaining useful life of a current asset, comprising the steps of: obtaining exemplar degradation data from at least two example assets; transforming the exemplar degradation data into functional approximations defining exemplar degradation paths; acquiring current degradation data from a current asset; evaluating the functional approximations defining the exemplar degradation paths at a current usage value to obtain expected degradation data; determining similarities between the current degradation data and the expected degradation data; and estimating, with a computer, a remaining useful life of the current asset using results of the determining step.
 24. A system for estimating a remaining useful life of a current asset, said system comprising: a computer configured to transform exemplar degradation data obtained from at least two example assets into functional approximations defining exemplar degradation paths; said computer configured to evaluate said functional approximations defining exemplar degradation paths utilizing current degradation data acquired from a current asset to obtain expected degradation data; said computer configured to classify said current degradation data acquired from the current asset as a function of similarity between said current degradation data and said expected degradation data; and said computer configured to estimate a remaining useful life value of the current asset using results of the classification of said current degradation data.
 25. A system for estimating a remaining useful life of a current asset, said system comprising: a computer configured to transform exemplar degradation data obtained from at least two example assets into functional approximations defining exemplar degradation paths; said computer configured to evaluate said functional approximations defining exemplar degradation paths utilizing current degradation data acquired from a current asset to obtain expected degradation data; said computer configured to determine similarities between the current degradation data and the expected degradation data; and said computer configured to estimate a remaining useful life value of the current asset using said determined similarities between the current degradation data and the expected degradation data. 